A-four-digit-whole-number-is-interesting-if-the-number-formed-by-the-leftmost-two-digits-is-twice-as-large-as-the-number-formed-by-the-rightmost-two-digits-for-example-2010-is-interesting-1-find-t

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Question Number 89878 by malwaan last updated on 19/Apr/20

$$\text{boldsymbol}A\text{boldsymbol}four\mathrm{\_}digit\text{boldsymbol}whole\text{boldsymbol}number$$$$\text{boldsymbol}is\text{boldsymbol}interesting\text{boldsymbol}if\text{boldsymbol}the\text{boldsymbol}number$$$$\text{boldsymbol}formed\text{boldsymbol}by\text{boldsymbol}the\text{boldsymbol}leftmost\text{boldsymbol}two$$$$\text{boldsymbol}digits\text{boldsymbol}is\text{boldsymbol}twice\text{boldsymbol}as\text{boldsymbol}large\text{boldsymbol}as\text{boldsymbol}the$$$$\text{boldsymbol}number\text{boldsymbol}formed\text{boldsymbol}by\text{boldsymbol}the$$$$\text{boldsymbol}rightmost\text{boldsymbol}two\text{boldsymbol}digits.$$$$\left(\text{boldsymbol}for\text{boldsymbol}example2010\text{boldsymbol}is\text{boldsymbol}interesting\right)$$$$1\text{boldsymbol}find\text{boldsymbol}the\text{boldsymbol}largest\text{boldsymbol}whole\text{boldsymbol}number$$$$\mathbb{B}\text{boldsymbol}such\text{boldsymbol}that\text{boldsymbol}all\text{boldsymbol}interesting$$$$\text{boldsymbol}numbers\text{boldsymbol}are\text{boldsymbol}divisible\text{boldsymbol}by\mathbb{B}$$$$2\text{boldsymbol}find\text{boldsymbol}the\text{boldsymbol}smallest\text{boldsymbol}whole$$$$\text{boldsymbol}number\mathbb{D}\text{boldsymbol}such\text{boldsymbol}that\mathbb{D}\text{boldsymbol}is$$$$\text{boldsymbol}divisible\text{boldsymbol}by\text{boldsymbol}all\text{boldsymbol}interesting$$$$\text{boldsymbol}numbers.$$

Commented by malwaan last updated on 19/Apr/20

$$1\mathbb{B}=201why?$$

Answered by malwaan last updated on 20/Apr/20

$$0201=201\times 1$$$$0402=201\times 2$$$$.$$$$.$$$$2010=201\times 10$$$$2211=201\times 11$$$$.$$$$.$$$$9648=201\times 48$$$$9849=201\times 49$$$$\Rightarrow 201\text{boldsymbol}is\text{boldsymbol}GCD$$$$\therefore \mathbb{B}=201$$

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